Near Queensland, the scenic Rees-Dart route is a 42 mile tramp typically taking three nights. Luckily, there are three huts about a days walk between. Or, if you are looking for a more primative experience, backcountry camping is permitted. Make sure to watch the weather before attempting to cross Rees Saddle.
Overall, Rees-Dart Route is the 14th most popular hiking trail of all 15 hikes in New Zealand.